Theorem e12

Description: A virtual deduction elimination rule (see sylsyld ). (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e12.1	|- (. ph ->. ps ).
	e12.2	|- (. ph ,. ch ->. th ).
	e12.3	|- ( ps -> ( th -> ta ) )
Assertion	e12	|- (. ph ,. ch ->. ta ).

Proof

Step	Hyp	Ref	Expression
1		e12.1	|- (. ph ->. ps ).
2		e12.2	|- (. ph ,. ch ->. th ).
3		e12.3	|- ( ps -> ( th -> ta ) )
4	1	vd12	|- (. ph ,. ch ->. ps ).
5	4 2 3	e22	|- (. ph ,. ch ->. ta ).